tikz: self loop with two arrows at the end (i.e. ending by ->>)

How to modify the following example to get a self loop labelled by "b" ENDING BY TWO ARROWS? The other self loop labelled by "a" should remains as it is.

\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,semithick]
  \node[initial,initial where=above,initial distance=4mm,accepting,state] (s) {s};
  \path
  (s)   edge     [loop right] node {$a$} (s)
        edge [->>,loop left] node {$b$} (s);
\end{tikzpicture}